This paper is devoted to a new integrable two-component Novikov equation, lax pairs and bi-Hamiltonian structures. Firstly, the local well-posedness in nonhomogeneous Besov spaces is established by using the Littlewood–Paley theory and transport equations theory. Then, we verify the blow-up that occurs for this system only in the form of breaking waves. Moreover, with analytic initial data, we show that its solutions are analytic in both variables, globally in space and locally in time. Finally, we prove that the strong solutions of the system maintain corresponding properties at infinity within its lifespan provided the initial data decay exponentially and algebraically, respectively.

本文致力于一个新的可积两分量Novikov方程，松散对和双哈密顿结构。首先，利用Littlewood-Paley理论和输运方程理论建立了非齐次Besov空间中的局部适定性。然后，我们仅以碎波的形式验证该系统发生的爆炸。此外，借助分析性的初始数据，我们证明了其解决方案可以对两个变量进行分析，无论是全局变量还是时间局部变量。最后，我们证明了该系统的强大解决方案在初始数据分别按指数和代数衰减的情况下，在其生命周期内的无穷远处保持了相应的属性。